Introduction:-The process of approximate reasoning in an NPS can be described as matching facts represented by their truth degrees against antecedents of rules. Then the truth values (certainty degrees) of the new facts (conclusions) are computed. This is repeated as a chain of inferring new facts, matching the newly inferred facts (and the old facts of course) to the productions again, and so forth.
The reasoning process is no monotonic; processing of new facts may decrease the certainty degree of an already inferred fact. The main idea of controlling the approximate reasoning in an NPS is that by tuning the inference control parameters we can adjust the reasoning process for a particular production system to the requirements of the experts. Approximate reasoning in an NPS is a consequence of its partial match. For example, by using the noise tolerance coefficients Qi, an NPS can separate facts that are relevant to the decision process from irrelevant facts. Rules with different sensitivity coefficients Pi react differently to the same set of relevant facts.
An NPS can work with missing data. One rule may fire even when some facts are not known. By adjusting the degrees of importance DIij we declare that some condition elements are more important than others and rules can fire if only the important supporting facts are known. Adjustment of the inference control parameters facilitates the process of choosing an appropriate inference for a particular production system.
ExampleA simple diagnostic production system with four manifestations, M1 through M4, three rules R1, R2, and R3, and three diagnoses D1, D2, and D3 is represented in an NPS as follows:
R1: Ml (10) M2 (2) →D1 (0.4, 0.8, 1.0, 0.9);
R2: M2 (8) M3 (7) → D2 (0.2, 0.3, 2.0, 1.0);
R3: M3 (10)-M4 (8) → D3 (0.7, 1.5, 0.8, 0.6);
Rule R2 is the most sensitive one to the facts, rule R1 is less sensitive, and R3 is least sensitive. The same distinctions apply to the reactiveness and certainty degrees of the productions. The noise tolerance threshold Q3 of the third rule is highest, which means that this rule needs more strong evidence to be activated. The final values for these coefficients are to be set after experiments with real data and consultations with experts who are supposed to evaluate the correctness of the inference process. The attached inference coefficients are used to represent uncertainties based either on a statistical or on a Heuristic evaluation. They can also be adjusted during the experiments.
For a concrete set of manifestation values, M1 = 0.8, M2 = 0.3, M3 = 0.5, M4 = -0.9, and for an output threshold of the PM 0.15, the inferred diagnoses are D1 = 0.9, D2 = 1.0, D3 = 0.0. It could be seen that even having the strongest evidence for its supporting facts M3 and M4, the third rule fails to infer anything. This is due to its low noise tolerance (high value of 03) and low sensitivity (high value of P3). The second production is very sensitive (low value of P2) and has a high noise tolerance (low value of P2), so it reaches its diagnosis with the highest certainty degree. The first rule reaches a high certainty degree because its most important manifestation M1 (DI11 = 10 > DI12 = 2) is strongly supported by the fact M1 = 0.8 in the WM.
The simple diagnostic rules may be extended to fuzzy diagnostic rules, when the manifestations and the diagnoses are given linguistic values, for example: If M1 is Strong and M2 is More-Or-Less-Small, Then D1 is Medium Implementing fuzzy production systems in an NPS.
